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In this paper we evaluate the performance of point and interval estimators based on the maximum likelihood(ML) method for the nonlinear simplex regression model. Inferences based on traditional maximum likelihood estimation have good asymptotic properties, but their performance in small samples may not be satisfactory. At out set we consider the maximum likelihood estimation for the parameters of the nonlinear simplex regression model, and so we introduced a bootstrap-based correction for such estimators of this model. We also develop the percentile and bootstrapt confidence intervals for those parameters as competitors to the traditional approximate confidence interval based on the asymptotic normality of the maximum likelihood estimators (MLEs). We then numerically evaluate the performance of these different methods for estimating the simplex regression model. The numerical evidence favors inference based on the bootstrap method, in special the bootstrapt interval, which was decisive in an application to real data., Competing Interests: The authors have declared that no competing interests exist.

In recent years, many works have addressed the proposal of new probability models by theoretic and applied reasons. Specifically, mixture models have been indicated to describe phenomena whose resulting data impose high flexibility. One drawback of these tools is the high number of parameters involved, which implies hard inference procedures. To outperform this gap, we propose a new model that is able to describe multimodal behaviors with only three parameters, called compound truncated Poisson gamma (CTrPGa) distribution. Some properties of the CTrPGa law are derived and discussed: hazard, characteristic and cumulative functions and ordinary moments. Beyond, moment estimation, maximum likelihood estimation (via the expectation maximization algorithm) and empirical characteristic function methods for CTrPGa parameters are furnished. The first of them may be reduced to solve one nonlinear equation, which facilitates its use. We perform a simulation analysis to compare the performance of the three estimation methods studied. Moreover, since the gamma distribution and its mixture versions are commonly used to characterize synthetic aperture radar (SAR) intensities, we perform some real experiments with SAR imagery. The results present evidence that our model is a reasonable assumption that can be taken into account in the pre-processing step of such images., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)